Title :
Bounds for solutions of the discrete algebraic Lyapunov equation
Author :
Tippett, Michael K. ; Marchesin, Dan
Author_Institution :
Centro de Previsao de Tempo e Estudos Climaticos, Inst. Nacional de Pesquisas Espaciais, Cachoeira Paulista, Brazil
Abstract :
A family of sharp, arbitrarily tight upper and lower matrix bounds for solutions of the discrete algebraic Lyapunov equation are presented. The lower bounds are tighter than previously known ones. Unlike the majority of previously known upper hounds, those derived here have no restrictions on their applicability. Upper and Lower bounds for individual eigenvalues and for the trace of the solution are found using the new matrix bounds. Sharp trace bounds not derivable from the matrix bounds are also presented.
Keywords :
Lyapunov matrix equations; covariance matrices; eigenvalues and eigenfunctions; stability; Lyapunov metrix; covariance matrix; discrete algebraic Lyapunov equation; eigenvalues; lower bounds; matrix bounds; stability; upper hounds; Atmosphere; Covariance matrix; Eigenvalues and eigenfunctions; Equations; Fluid dynamics; State estimation; Upper bound;
Journal_Title :
Automatic Control, IEEE Transactions on
